There are three coordinate systems, which are galactic coordinates, the celestial coordinates and laboratory coordinates. The virial velocity direction is defined as a direction of 270\(^\circ \)  longitude and 0\(^\circ \)  latitude in galactic coordinates. We use the coordinate convert tool from the official NASA website (NASA LAMBDA–Tools), to convert the direction of the axion velocity from galactic coordinates to celestial coordinates. The axion velocity in celestial coordinates can be written as \(\mathbf {v}=\vert \mathbf {v} \vert (\cos \delta \cos \eta \mathbf {X}+ \cos \delta \sin \eta \mathbf {Y}+ \sin \delta \mathbf {Z})\) ,
where declination is \(\delta =-48^\circ \)  and right ascension is \(\eta =138^\circ \)  [1]}, [2]}.
